Representative Intensity Decays

There are two widely used methods for measuring fluorescence lifetimes, the time-domain and frequency-domain or phase-modulation methods. The basic principles of time-domain fluorometry are described in Chapter 1, Vol.l of this series(34) and those of frequency-domain in Chapter 5, Vol. 1 of this series.<35) Good accounts of time-resolved measurements using these methods are also given elsewhere/36,37) It is common to represent intensity decays of varying complexity in terms of the multiexponential model... 

We determine the SCP as it is terminated at the substrate in the following manner. First, we calculate I = dl/dt for the linear portion of the intensity decay. A°linear least squares fit to the data in the time interval 170 - 190 sec produces a value of dl/dt = 1150 counts/sec. This represents the steady state quenching rate which is intimately related to the steady state SPR. Secondly, we calculate I. = dl/dt at one-second intervals as the steady state endsrwith the arrival of the SCP at the substrate. For example, for the data in Figure 2,... 

The principles of time-resolved fluorometry are illustrated in Fig. 7.4. The d-pulse response of a fluorescent sample (i.e. the fluorescence intensity decay in response to an infinitely short light pulse mathematically represented by the Dirac function <5(t) delta excitation) is, in the simplest case, a single exponential whose time constant is the excited-state lifetime, but more frequently it is a sum of discrete exponentials, or a more complicated function sometimes, the system is characterized by a distribution of decay times. For any excitation function E(t), the response R(t) of the sample is the convolution product of this function by the <5-pulse response ... 

Figure 37 presents data of Robinson for tungsten surfaces. The dashed lines represent the decay of the diffracted intensity predicted by Eq. (38) and clearly there are significant discrepancies with the experimental values (open circles). If a roughness factor is introduced (Robinson used a partial occupancy model), the data can be fit quite well (solid lines). 

According to these expressions, the intensity of the OH emission will decay as a biexponent, the rapid initial phase 72 represents the reaction as it proceeds until the velocity of dissociation and recombination become equal. The slower phase 71 represents the decay when the two populations (< >OH and 0 ) are in equilibrium with each other. The relative amplitudes of the two phases Ar = (a2i — 7i)/(72 7i) and the macroscopic rate constants (71,72) allow one to calculate the rate of all partial reactions. The agreement between rate constants calculated by time-resolved measurements and steady-state kinetics is usually good. In a limiting case, where the rate of recombination is much slower than dissociation pKo > pH >> pK, the amplitude of the slow phase representing recombination will diminish to zero and the emission of the < >OH state will decay in a single exponent curve with a macroscopic rate constant 72 = k + %,nr) k. ... 

Further modifications have to be introduced in order to describe correctly the observed intensity decay for both signs of the scattering angle. In Eq. (10),/(D ) represents a Gaussian distribution of Dy around the mean value Dyo, which was obtained from the parabolic fit. Nl/r is a sign-dependent scaling factor, and in addition a roughness a is introduced. 

Fig. 19. Frequency-domain intensity decay of oxytocin at 20 C. The symbols ( ) represent the data, the solid line the best three-exponential fit, and the dashed line the best one-exponential fit. The lower panels show the deviations between the data and the calculated values for the one (a) and three ( ) decay time models. The values of Xr 377, 5.9 and 2.1 for the 1, 2 and 3 exponential fits, respectively.

The integrated area under the SIMS intensity decay curve is a measure of the total number of ions detected in a SIMS experiment. The total nimiber of ions detected for the species x can be written as Nj(x) = P NJ[x) T x) D x) where N x) is the number of molecules of x in the area analyzed, T(x) is instrument transmission for x, D x) is the detector efficiency for x, and Pf is the transformation probability. represents the probability that a molecule, M, sputtered from the surface will be detected as an ionic species, x. 

CU represent the fractional amount of flucvoi tm in eadi enndronmrat. Hence, for the protein shown in Hguie 4.4, one expects tti ttz a 0.5. The presoice of twodecay times results in curvature In the plot of log /(r) versus time, represented by the dashed line in the upp plot. The g< l of the intensity decay measurements is to recover the decay times (Xi) and amj itudes (ad from the /(r) measuremrats. 

Th e are many subtleties in TCSPC which are not obvious at fust examination. Why is the photem counting rate limited to one photon per 100 las pulses Present electronics feu TCSPC only allow detection of the first arriving photon. Once the first photon is det ted, the dead time in the electronics prevents detection of anoth photon resulting from the same excitation pulse. Recall that onis-slon is a random event. Following the excitation pulse, mc e photons are emitted at early times than at late times. If all could be measured, then the histogram of arrival times would represent the intensity decay. However, if many arrive, and only the first is counted, then the intensity decay is distorted to shorter times. This effect is described in more detail in Section 4.5.F. 

In our opinion, a three-component mixture with less than a threefold range in lifetime represents the practical limit of resolution for both TD and FD measurements. Analysis of the data from such a sample illustrates important considerations in data analysis at the limits of resolution. FD intensity decay data for the mixture of indole (4.41 ns), anthranilic acid (8.53 ns), and 2-aminopurine (11.27 ns) are shown in Figure 5.20. The data can not be fit to a single decay time, resulting in xJ = 54.2, so this model is easily... 

Estimation of the Spectral Relaxation Time Figure 7.41 shows time-dependent intensity decays of TNS bound to egg lecithin vesicles. The wavelengths of 390, 435, and 530 nm are in the blue, center, and red regions of the emission spectrum. Use the data in Figure 7.41 to calculate the spectral relaxation time for the TNS-labeled residue. Assume that the emission at 390 nm is dominated by the initially excited state (F) and that the emission at 435 nm represents the TNS, unaffected by relaxation. Interpretation of Wavelength-Dependent Lifetimes-. TNS was dissolved in various solvents or bound to vesicles of... 

The difficult in resolving (he two intensity decay components is illustrated by the intensity decay of tryptophan at pH 7 (Figure 17.4). The light source was a cavity-dumped rhodamine 6G dye laser, which was frequency-doubled to 29S nm and provided pulses about 7 ps wide. The detector was an MCP PMT detector. This confign-ration of high-speed components represents the state of the art for TCSPC measurements. The data were fit to the single- and double-exponential models,... 

DAS have been determined for a number of proteins, with an emphasis on proteins which contain two tryptophan residues. In these cases one hopes that each tryptophan will display a single decay time, so that the I S represent the emission spectra of the individual residues. One example is provided by a study of yeast 3-phospho-glycerate kinase (3-FGK), which has two tryptophan residues. Rom a number of pH- and wavelengdi-dependent measurements, the 0.6-ns component in die decay was associated with one residue, and the 3.1- and 7.0-ns components were associated widi die second tryptophan residue. The wavelength-dependent intensity decays were... 

The D-A transfer can speed up the decay of D in its excited state and thus shorten the decay time of D. As a result, r/g can also be obtained from the decay curve of the D luminescence after flash excitation of D. The decay curve represents the decay of transient luminescence intensity, which can be regarded as the number of photons emitted per time at time t. Denote the D-luminescence decay function by Io(t) for the absence of A and by I t) for the presence of A. The decay function can be obtained by normalizing the initial intensity of the experimentally measured luminescence decay curve, meaning 7o(0) = 7(0) = 1. The integrals of the intensity-decay function over time are proportional to the number of total photons emitted after excitation, i.e., it is just the measure of the steady-state luminescence intensity. From Eqs. (3.1) and (3.2), one thus has [4]... 

Therefore the intensity decays exponentially after the initial excitation pulse. The fluorescence lifetime of the excited state, can be represented as Tp = (l/kp). The fluorescence lifetime of a molecule is defined as the time taken for the excited state population to fall to 1/e of that initially excited. Equation (1.11) can then be rewritten as... 

The model [39] was developed using three assumptions the conformers are in thermodynamic equilibrium, the peak intensities of the T-shaped and linear features are proportional to the populations of the T-shaped and linear ground-state conformers, and the internal energy of the complexes is adequately represented by the monomer rotational temperature. By using these assumptions, the temperature dependence of the ratio of the intensities of the features were equated to the ratio of the quantum mechanical partition functions for the T-shaped and linear conformers (Eq. (7) of Ref. [39]). The ratio of the He l Cl T-shaped linear intensity ratios were observed to decay single exponentially. Fits of the decays yielded an approximate ground-state binding... 

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